please explain when we use double integral for finding the volume and when we use triple integral for that ?

Answer 1

When we use a double integral to solve for volume, the value being integrated is the range of the third variable. Integrate 1 over the range of the third variable, and you've converted the double integral into a triple integral. The most logical time to have a triple integral might be when all three variables are expressed in terms of a fourth variable. Note that we sometimes use single integrals (volumes of revolution) and sometimes no integrals at all (volume of a 3-d object with formula where we know the values to substitute). With a parallelepiped, we can get the volume by calculating a determinant.